EMB120 CREW RECEIVES TCASII TA DURING SIMULTANEOUS PARALLEL DEPS AT LAX.

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LEAVING LAX ON THE VENTURA 2 DEP ENRTE TO SANTA ROSA; CA. IT WAS NIGHT AND THE SKY WAS CLR WITH APPROX 7 MI VISIBILITY. WE WERE INSTRUCTED BY TWR TO CROSS RWY 24L AND HOLD SHORT AT RWY 24R. A JETSTREAM WAS INSTRUCTED TO TAXI ONTO RWY 24L AND WE WERE THEN GIVEN POS AND HOLD ON RWY 24R. I WAS AWARE THAT OFTEN THE LAX TWR WILL ALLOW PLANES TO DEPART FROM THE LAX NORTH COMPLEX ENRTE TO A DEST S OF LAX SO AS TO SAVE TAXI TIME. THIS RWY ARRANGEMENT (ACFT Y ON THE L AND US ON THE R) APPEARED TAILOR MADE FOR OUR WBOUND DEP AND AN ACFT Y SBOUND DEP. ACFT Y WAS CLRED FOR TKOF AND IMMEDIATELY THEREAFTER WE WERE ALSO CLRED FOR TKOF WITH INSTRUCTIONS TO CLB TO 3000 FT AND TURN R TO 270 DEGS AT THE LAX VOR. IMMEDIATELY AFTER ROTATING; TWR ASKED IF WE HAD ACFT Y IN SIGHT. WE REPLIED THAT WE DID AND WERE INSTRUCTED TO MAINTAIN VISUAL SEPARATION AND CONTACT DEP CTL. WE CONTACTED DEP; BROUGHT THE FLAPS UP AND BEGAN OUR TURN WITH THE APPROPRIATE AIRSPD TO 270 DEGS. AT THIS TIME; DEP ASKED US TO VERIFY ACFT Y IN SIGHT. WE CALLED THEM IN SIGHT AND IT BECAME APPARENT THAT THEY WERE OBVIOUSLY HEADING IN THE SAME DIRECTION. THEY TOO WERE GIVEN A R TURN ABEAM THE VOR TO 270 DEGS IN FRONT OF US. OUR FASTER SPD IN THE CLB AND IN THE TURN PUT US NEAR THE JETSTREAM THAT HAD ALREADY MADE THE TURN TO 270 DEGS. I HAD VISUAL CONTACT WITH THE PLANE; HOWEVER; AT NIGHT THE DEPTH PERCEPTION WAS DIFFICULT TO JUDGE HAVING ONLY THEIR LIGHTS TO GO BY. WE WERE GIVEN FURTHER CLB TO 7000 FT. DEP ADVISED ACFT Y THAT WE WERE CLBING ABOVE THEM AND THAT THEY SHOULD STOP CLB AT 4000 FT. WE BEGAN TO OVERTAKE THEM AND I FELT UNCOMFORTABLE WITH THE SEPARATION; AS IT BECAME OBVIOUS THEY WERE EITHER GOING IN OUR SAME DIRECTION OR HEADING NBOUND. I INCREASED THE RATE OF CLB AND ABOUT THAT TIME WE GOT A TCASII ALERT. THE ALERT QUICKLY SILENCED AS WE CLBED ABOVE THEM. AT THAT TIME DEP TURNED ACFT Y UNDERNEATH US ON A NBOUND HEADING. SHORTLY THEREAFTER WE WERE BOTH INSTRUCTED TO CONTACT THE NEXT SECTOR FREQS.